How to solve

Use calculus to find a value for the $($unknown$)$ constant $k$ so that the parabola $y=x^2+k$ is tangent to the unit circle at $2$ points $($as shown in diagram$).$

Recall that the unit circle is described by the equation $x^2+y^2=1.$

It will help to know that the circle and the parabola must share a tangent line at each intersection point.